In some aspects of image recognition, access to blurred messages occurs. The need to read these occasional anomalies is obvious but present means often require time-consuming digital procedures using the various algorithms such as LaPlacian, high-pass filtering and others currently available.
One of the "standard" approaches of both optical and digital is to use an inverse filter. That is, in an optical system or its digital equivalent, one takes a Fourier Transform of the blurred image and places a filter whose character is to be determined in the Fourier or spatial frequency plane. If properly designed, the filter upon reimaging (taking another Fourier Transform) will bring a degree of restoration to the image, rendering it understandable. That means perfect restoration (in one or more operations) is not necessary, or sometimes not even possible. The basis of restoration is summarized in the following sequence of equations:
g(x.sub.2,y.sub.2)=complex amplitude of image PA1 h(x.sub.1,y.sub.1 ;x.sub.2,y.sub.2)=impulse response PA1 f(x.sub.1,y.sub.1)=complex amplitude of object PA1 1--word length determination PA1 2--word length location and isolation PA1 3--sentence identification PA1 4--paragraph identification PA1 5--intercolumn location PA1 6--single upper, center, and lower letter zone identification and location, and PA1 7--digram and trigram identification and location.
g=f*h PA2 G=F H PA2 G H.sup.-1 =F H H.sup.-1 PA2 G H.sup.-1 =F (Restored image)
where the capital letters refer to the Fourier Transforms of the corresponding functions and (*) denotes convolution. The result, in principle, is the inverse filter which, when inserted in the Fourier plane, should provide image restoration.
In FIGS. 1A and 1B we can see pictorially what is done. In FIG. 1A we have the absolute value of amplitude for an image with the modulus of the inverse filter shown in FIG. 1B. In the simplest case the first and third orders would have negative phase and the second and fourth, positive. In reality the spectrum amplitude and phase are much more complicated in distribution throughout the spatial frequency domain.
Much work has been and is being done principally in the digital analysis world with such techniques as contrast enhancement routines, constrained least squares filtering, extended filters, optimizing mean square error filters, and other extensions or alterations of the Wiener filter. The work also includes the standard digital fare like high-pass filtering with convolution matrices, establishing median filters wherein each pixel is processed by giving it the median of its eight neighbors (in a 3.times.3 matrix) and Kalman filtering with various kernels. In others, adaptive filtering is performed. This is a technique of performing a large number of iterations of, in sequence, the Fourier Transform, assessment, modification, inverse transform, assessment, Fourier Transform, modification, and so forth. A priori knowledge or good guessing drive the modifications in the sequence. In some iterative routines, the investigator assumes that the degradation must lie between or within a set of parameters and uses these to make appropriate modifications based upon this.
Although the system of my co-pending application Ser. No. 08/351,707 is capable of restoring blurred images, it is believed that the present invention directed to word processing is more efficient. This is due to the fact that larger segments generally require the use of Fourier plane processing. In this case we would process signals like: EQU (w.sub.1 +w.sub.2 +w.sub.3 . . . )(w.sub.1 +w.sub.2 +w.sub.3 . . . )*=w.sub.2.sup.2 +w.sub.2.sup.2 . . . +w.sub.1 w.sub.2 +w.sub.2 w.sub.1 +
i.e., we would have complex intraword/intrasentence terms in addition to the word and sentence terms themselves making the process of sorting amplitudes and phases of an inverse filter more demanding than most applications warrant.